Flat-ended Projectiles Research Articles

Failure mechanisms in impacting penetrators

Experiments are described on (i) the simple Taylor test where a flat-ended projectile mushrooms against a semi-infinite “rigid target”, (ii) penetration of conically tipped cylindrical projectiles into semi-infinite targets, (iii) the use of modified nose geometries to direct the pattern of shear failure and (iv) the impact of balls on thin plates. Macro- and micro-structural investigation of fractured penetrators illustrates mechanisms of ductile fracture, intergranular and transgranular brittle fractures, and adiabatic shear. Stress analysis highlights those regions subjected to prolonged hydrostatic tensile stresses during impact indicating fracture by spalling, and those regions where persistent velocity discontinuities or planes of maximum shear strain rate indicate adiabatic shear failure.

A note on the deformation of conical penetrators

Conical penetrators have been shown to give enhanced penetration over flat-ended projectiles up to a certain transition velocity. This transition velocity was found to be associated with a separation of the conical nose from the penetrator body which caused the penetrator to revert to the behaviour of a flat-ended penetrator at higher velocities. An explanation of the marked deformation resistance of the conical noses of these penetrators is presented.

Projectile Impact Ignition Characteristics of Propellants III. Effect of Particle Size and Porosity

Abstract An investigation of the effect of particle size and material porosity on the projectile impact sensitivity of a composite explosive propeliant is described. The tests consisted of impacting small cylinders of the propeliant with flat-ended projectiles of different diameters fired from guns at various velocities, and observing the impact reaction by an open-shutter camera, photocell, post inspection and weighing of propeliant fragments. The observed general behavior of the propeliant samples containing porosity and (independently) large explosive particles was similar to that obtained with the standard propeliant. The porosity sensitized the propeliant to both burning and detonation at large projectile diameter, but the effect was relatively small. At small diameter the effect was negligible. On the other hand, the presence of large particles had a very great effect on sensitizing the propeliant at all projectile diameters.

An analytical solution of G. I. Taylor's theory of plastic deformation in impact of cylindrical projectiles and its improvement

The theory of plastic deformation in the impact of cylindrical projectiles on rigid targets was first introduced by G. I. Taylor (1948)[1]. The importance of this theory lies in the fact that the dynamic yield strength of the materials can be determined from the measurement of the plastic deformation of flat-ended cylindrical projectiles. From the experimental results[2] we find that the dynamic yield strength is independent of impact velocity, and that it is higher than the static yield strength in general, and several times higher than the static yield strength in certain cases. This gives an important foundation for the study of elastoplastic impact problems in general. However, it is well known that the complexity of differential equations in Taylor's theory compelled us to use the troublesome numerical solution. In this paper, the analytical solution of all the equations in Taylor's theory is given in parametrical form and the results are discussed in detail.

温度こう配をもつ棒内を伝ぱする弾塑波の計算機シミュレーション

The problem of a cylindrical flat-ended projectile impinging on a flat rigid anvil has been analyzed by many investigators in order to assess the dynamic stress-strain relation at high strain rates. Though impact speed in the method described above is higher than those of other tests such as Split Hopkinson Bar Method, the temperature rise caused by plastic work cannot be neglect in this method. Such temperature rise creates nonhomogeneity in the loading region and this nonhomogeneity is maintained almost constant in the unloading region.In this paper, the simulation of elasto-plastic waves propagated in a finite bar, which impinged on a flat rigid anvil, with steady temperature gradients was made by a computer. The temperature distribution was assumed to be an exponential function of the axial distance of the bar. A constitutive equation used in the analysis was a rate-dependent type and it was assumed that the static stress was a linear function of absolute temperature. The problem was formulated and solved numerically by the method of characteristics with supplement rectangular net.The numerical results show that the temperature distribution has influence upon stress and strain. Especially, it has considerable influence upon the deformation resistance and unloading wave from the free end.

Projectile Impact Ignition Characteristics of Propellants I. Deflagrating Composite Explosive

Abstract The results of an investigation of the projectile impact sensitivity of a deflagrating composite explosive are described. The tests consisted in impacting small cylinders of the propellant with flat-ended projectiles of different diameters fired from guns at various velocities, and observing the impact reaction by an open-shutter camera, photocell, post inspection and weighing of the propellant fragments. The critical ( minimum) impact velocity required to produce a sustained reaction in the propellant decreased with increasing projectile diameter. The nature of the reaction depended on the diameter. At small diameters, the induced reaction was always detonation; whereas at the largest diameter the reaction was deflagration, whose intensity increased with increasing impact velocity. A higher critical velocity then again resulted in detonation. A model based on hot spot initiation in which a pressure-dependent effective hot spot concentration determines the rate of buildup of reaction after igniti...

A numerical method of analysis for the mushrooming of flat-ended projectiles impinging on a flat rigid anvil

The theories of Taylor, and Lee and Tupper use conservation of momentum across the plastic wave front to determine the strain distribution in a flat ended projectile impinging on a flat rigid anvil. In Hawkyard's theory conservation of energy is used across the plastic wave and some account of projectile strain hardening is incorporated. The present study replaces the projectile with a lumped parameter model which consists of a number of concentrated masses connected to each other by massless links. The equation of motion is applied to each concentrated mass and a solution for the dynamic behaviour of the connected mass system is obtained using a numerical technique. This method of approach is capable of incorporating the effects of material strain hardening and strain rate on the final shape of the projectile, it enables the distribution of strain in the projectile to be determined.

Penetration of targets by flat-ended projectiles

A model is presented which describes plug formation in the penetration of targets by flat-ended projectiles travelling at sub-sonic speeds. The model assumes that the plug is accelerated by elastic and plastic stress waves and that the plug-target shear and the projectile-target shear occurs at constant shear stress. The failure criterion adopted is based on the separation of the plug from the target by plastic shearing. Calculations of critical velocities for expulsion of the plug and of plug thickness at the critical velocities agree well with experimentally determined values. Above the critical velocities, the model predicts plug exit velocities well, although the plug thicknesses are less than experimental values obtained on the softer target materials. A discussion of this discrepancy and of the assumptions used in the model is given.

An examination of the effect of target thickness in the perforation of mild steel plate by a flat-ended projectile

Results of experiments on the high-speed perforation of different thicknesses of mild steel plate are presented, for impact velocities of up to 300 m/sec, and compared with the results of static perforation tests. Plate profiles, thinning of perforated plugs and energy requirements for perforation, are presented and discussed. It is found that the bulging of the target plate is greatest when the projectile is just contained, and that the bulging at containment increases with plate thickness over the early stages of the thickness range, after which it decreases with increasing plate thickness. This is contrary to the static case, in which the bulging continually increases. A photomicrograph of the material at the plug-plate interface is provided to support the view that thermo-plastic instability occurs when perforating thicker plates at high speed.

The influence of projectile geometry on adiabatic shear and target failure

An examination has been carried out of the ability of projectiles of three different geometries to perforate plates of an age hardened aluminum alloy. It was found that flat-ended projectiles perforate the target with greater ease than projectiles with more rounded ends. The results are discussed in terms of the ability of a particular projectile geometry to promote adiabatic shear during penetration and the mode of fracture when projectile breakout occurs.

A theory for the mushrooming of flat-ended projectiles impinging on a flat rigid anvil, using energy considerations

The well-known theory of Taylor1 for the mushrooming of flat-ended projectiles uses a momentum equilibrium equation across the plastic wave front, as a basis for the analysis of the strain distribution. An analysis is now presented which employs basically the same approach as Taylor's in the general simplifying concepts of the process, but applies instead an energy equilibrium equation across the plastic wave. The resultant equations defining the final geometry are of simple form and the profiles predicted appear to be in closer agreement with experiment than are given by Taylor's theory. The present theory is developed to take some account of strain hardening, which appears to affect considerably the final profile. Essential differences between the present energy-based theory and Taylor's momentum-based theory are discussed.

The mean dynamic yield strength of copper and low carbon steel at elevated temperatures from measurements of the “mushrooming” of flat-ended projectiles

Mean dynamic yield strengths for copper and mild steel are deduced from strain measurements on the “mushroomed” ends of flat-ended projectiles, after impact on a flat, nominally rigid anvil. The kinetic energy at impact is equated with plastic work, to give a mean dynamic yield strength averaged over the deformed specimen. Experiments are carried out over the temperature range 20–700°C, with impact velocities in the region of 600 ft/sec, giving a mean strain rate estimated at 5 × 10 3/sec. The yield stress-temperature results obtained show an abrupt increase in dynamic/static mean yield stress ratio at homologous temperatures, T T M , of 0·4 for steel and 0·5 for copper. These results agree generally with the findings from other investigations into high-speed blanking 5 and indentation. 7 Existing theories for the mushrooming of flat-ended projectiles 1, 3 do not predict the profiles actually obtained in the present experiments.

The use of flat-ended projectiles for determining dynamic yield stress III. Changes in microstructure caused by deformation under impact at high-striking velocities

The mechanism of deformation of metals at high velocities has been studied by examining the microstructure of cylinders of mild steel, duralumin and standard silver (of composition Ag 92.5%, Cu 7.5%) of similar hardness, and of steel balls after impact on steel plates at velocities from 300 to 3830 ft. /sec. The means by which the stress on impact was relieved depended on the material, and was first the formation of twins or ‘compression bands’, i. e. by block movement of wedges of material within individual grains, or by cracking. When the applied stress could no longer be relieved in this way, plastic deformation occurred. The amount of residual strain in deformed mild steel and duralumin has been examined by observing changes of microstructure after annealing. Hardness surveys were made on longitudinal sections of the cylinders and the results correlated with the microstructures and with observations of the limits of strain due to impact.

The use of flat-ended projectiles for determining dynamic yield stress I. Theoretical considerations

It has long been known that metals may be subjected momentarily to stresses for exceeding their static yield stress without suffering plastic strain. One of the simplest methods for subjecting a metal to a high stress for a short time is to form it into a cylindrical specimen and fire this at a steel target. The front part of this projectile crumples up, but the rear part is left undeformed. If the target is rigid the distance which this portion travels while it is being brought to rest may be taken as the difference between the initial length and the length of the deformed specimen after impact. Knowing the velocity of impact, a minimum possible value can be assigned to the maximum acceleration of the material, and from this a minimum value for the yield stress can be calculated. The actual yield stress is considerably greater than this minimum, and methods are given for calculating a more probable value.

The use of flat-ended projectiles for determining dynamic yield stress - II. Tests on various metallic materials

A description is given of the experimental technique devised to apply the method outlined theoretically in part I to the measurement of the dynamic compressive yield strength of various steels, duralumin, copper, lead, iron and silver. A polished piece of armour steel was employed as a target, and cylindrical specimens were fired at it at various measured velocities from Service weapons. The distance between the weapon and target was made short to ensure normal impact, and apparatus was devised for the precise measurement of striking velocity over this short range. The dynamic compressive yield strength was computed from the density of the specimen, the striking velocity, and from measurements of the dimensions of the test piece before and after test. Details are given of the accuracy of the various measurements, and of their effect on the values of yield strength. The method was found to be inaccurate at low and high velocities. For instance, with mild steel, satisfactory results were only obtainable within the range 400 to 2500 ft. /sec. The range of velocities within which satisfactory results could be obtained varied with the quality of the material tested, soft metals giving results within a much lower range than that necessary for harder materials. Because of its failure at low velocities, the method could not be employed to bridge the gap between static and dynamic tests. The rate of strain employed in the dynamic tests could not be measured, but was estimated to be of the order of 10,000 in. /in. /sec. With the materials tested little change of dynamic strength occurred within the range of striking velocities employed, probably because the rate of strain did not vary to any great extent with the striking velocity. Within the range of weapons available, that is, from a 0·303 in. rifle up to a 13 pdr. gun (calibre 3·12 in.), little change of dynamic strength occurred with alteration of the initial dimensions of the specimens, probably because the corresponding change of rate of strain was not large. In general, the dynamic compressive yield strength S was greater than the static strength Y represented by the compressive stress giving 0·2% permanent strain. For steels of various types, regardless of chemical composition and heat treatment, there was a relation between S / Y and the static strength Y , the ratio decreasing from approximately 3 when Y was 20 tons/sq. in. to 1 when Y was 120 tons/sq. in. A similar relation occurred with duralumin, S / Y varying from 2·5 at Y = 8 tons/sq. in. to 1·4 at Y = 25 tons/sq. in. Dynamic compressive yield values were obtained for soft materials such as pure lead, copper and Armco iron, which, under static conditions, gave no definite yield values. A plot of the unstrained length of the specimen X , expressed as X / L (where L = initial overall length), versus the final overall length L 1 , expressed as L 1 / L , was made for the various materials. Any specified value of X / L was associated with greater values of L 1 / L for the more ductile materials, such as copper and lead, than for the brittle materials, such as armour plate and duralumin.